Again, the leading term of the gauge identity is given by the free
contribution. This agrees with the concept of interaction
consistency. At the final step of analysis, we verify that the
physical degrees of freedom number is preserved by the coupling.
Equation (8) of paper [1]} expresses the physical degrees
of freedom number via the orders gauge symmetries, gauge identities,
and equations of motion in the involutive of dynamics. The systems
(REF ), (REF ) are involutive, and they have equal
orders of gauge symmetries, gauge identities and equations of
motion. So, they have to poses one and the same physical degrees of
freedom number. All the above implies that the non-Lagrangian
interaction (REF ) is consistent for the general values of
the parameters \(\beta ,\alpha \) .
